Difference between revisions of "009C Sample Final 3, Problem 8"

Revision as of 14:52, 5 March 2017

A curve is given in polar coordinates by $r=4+3\sin \theta$

0\leq \theta \leq 2\pi

(a) Sketch the curve.

(b) Find the area enclosed by the curve.

Foundations:
The area under a polar curve $r=f(\theta )$ is given by
$\int _{\alpha _{1}}^{\alpha _{2}}{\frac {1}{2}}r^{2}~d\theta$ for appropriate values of $\alpha _{1},\alpha _{2}.$

Solution:

(b)

Step 2:

Final Answer:
(a)
(b)

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+|The area under a polar curve &nbsp; <math style="vertical-align: -5px">r=f(\theta)</math>&nbsp; is given by
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+&nbsp; &nbsp; &nbsp; &nbsp;<math>\int_{\alpha_1}^{\alpha_2} \frac{1}{2}r^2~d\theta</math>&nbsp; for appropriate values of &nbsp;<math>\alpha_1,\alpha_2.</math>
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